Research ArticlePHYSICS

Nonmonotonic contactless manipulation of binary droplets via sensing of localized vapor sources on pristine substrates

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Science Advances  30 Sep 2020:
Vol. 6, no. 40, eaba3636
DOI: 10.1126/sciadv.aba3636
  • Fig. 1 Binary droplets under an external vapor source: attraction versus repulsion.

    (A) Schematics of the contactless manipulation of binary droplets on solid substrates with an external localized vapor source: We placed a binary droplet (radius RD; contact angle θc) at a distance xs from a blunt needle (inner radius Rs) from where water vapor diffuses; zs is the distance between source and substrate. We performed all experiments within an environmental chamber with controlled temperature (T = 21 ± 0.5 ° C) and relative humidity (RH = 50 ± 5%). (B and C) Time sequences showing a 0.5-μl binary droplet of water and PG (RD = 1.38 ± 0.06 mm; θc = 12.5 ± 0. 7; mole fraction of water xH2O = 0.95) being (B) attracted to or (C) repelled from the source (Rs = 350 μm) depending on the initial separation xs: (B) xs = 2 mm (movie S1) and (C) xs = 0 (movie S2). The horizontal and vertical dashed lines highlight the substrate and the center of the vapor source, respectively. Scale bars, 1 mm. (D) Time evolution of xs converging to the same radial distance xe (dashed line) from the source for the droplets in (B) (circles) and (C) (triangles).

  • Fig. 2 Forces induced on the contact line of binary droplets under an external vapor source.

    An external vapor source induces gradients of surface tension γ on a binary droplet’s free surface. The corresponding Marangoni flows generate forces on the droplet’s contact line, ultimately leading to its motion toward or away the vapor source. (A) Estimated change of surface tension γ along the droplet’s free surface due to vapor sources (black dots, Rs = 350 μm) placed directly above (xs = 0), with a slight offset (xs = 0.6RD) and afar from (xs = 1.2RD) the droplet when evaporation starts. The change in γ is given relative to a reference value γRH estimated removing the effect of the source in Eq. 2, i.e., by imposing pH2O = pRH. Dashed lines, meridians through the droplets’ apices. The coordinate unit vectors correspond to 0.5 mm. (B) Calculated local force (blue arrows) along the contact line (gray circles) due to vapor sources as in (A) (red circles). Force vectors, shown every π10, are integrated over π500 intervals along the contact line.

  • Fig. 3 Calculated net viscous driving force exerted on binary droplets by an external vapor source.

    Calculated viscous driving force Fxγ (Eq. 5) exerted on the droplet by the vapor source as a function of the distance xs from the source and time t from the beginning of the evaporation for increasing source radii Rs. The solid lines represent the time evolution of the droplet’s radius RD (fig. S2B).

  • Fig. 4 Droplet’s velocity in experiments and model.

    Droplet’s mean velocity vx with distance xs from the source and time t from when evaporation starts for increasing Rs (Rs = 150 μm, Rs = 210 μm, and Rs = 350 μm) in experiments and simulations. Mean values are averages of at least five different experiments with a SD of 0.5 μm s−1 at Rs = 150 μm, 0.8 μm s−1 at Rs = 210 μm, and 1.5 μm s−1 at Rs = 350 μm. We performed these experiments by continuously moving the stage to keep the distance between source and droplet fix at an initial set value xs (see Materials and Methods). The solid lines represent the time evolution of the droplet’s radius RD (fig. S2B). In the model values, the dashed lines delimit the part where corresponding experiments are available. In the experiments for Rs = 350 μm, the circles represent three trajectories of individual droplets moving toward the source from xs = 2 mm (as in Fig. 1B) at different times (fig. S4): (I) 30 s, (II) 250 s, and (III) 500 s from the beginning of their evaporation. The color code of each circle represents the droplet’s velocity at a given time.

  • Fig. 5 Printing with moving droplets.

    (A) Photographs of linear polymer deposits (PVOH) from moving water/PG droplets (VD = 0.5 μl, xH2O = 0.95) with decreasing PVOH concentrations. (B) Typical height profiles for the deposits in (A) (see Materials and Methods). a.u., arbitrary units. (C) Deposit maximum line width w as a function of droplet’s volume and PVOH concentration, averaged across at least three deposits. The dashed lines are fits to the experimental data showing the proportionality between w and VD1/3. (D and E) Stitched photographs of PVOH deposits ([PVOH] = 2 mM) from moving water/PG droplets (VD = 0.1 μl, xH2O = 0.95) guided along 2D patterns to form (D) a serpentine with an ≈30-μm interline spacing (movie S3) and (E) the letters ucl (movie S4). (F) Example photograph (enhanced with an edge-aware filter for contrast) of alignment in linear polymer deposits ([PEG] = 100 mM) from moving water/PG droplets (VD = 0.5 μl, xH2O = 0.95) guided at 8 μm s−1 (see Materials and Methods and movie S5). Figure S6 shows higher speeds. All PVOH droplets contain rhodamine B for visualization. We subtracted the background from all color images. In the photographs, black triangles indicate the direction of motion. Scale bars, 1 mm.

  • Fig. 6 Chemical reactors with moving droplets.

    (A) Stitched photographs of color gradients in polymer deposits obtained by retracing water/PG droplets (VD = 0.25 μl, xH2O = 0.95, [PVOH] = 4 mM) containing 30 mM bromothymol blue over previous deposits by droplets (VD = 0.15 μl, xH2O = 0.95, [PVOH] = 2 mM) containing different NaOH concentrations (movie S6) (see Materials and Methods). Black triangles indicate the direction of motion. (B and C) Time sequences showing coalescence of two water/PG droplets (VD = 0.5 μl, xH2O = 0.85) controlled by two vapor sources (Rs = 640 μm) (see Materials and Methods). Droplets start coalescing at 0 s and remain visibly compartmentalized for a long time as confirmed by the flow lines in fig. S7. In (B), the droplets contain 100 mM NaOH and a dye, either methyl red (yellow, left) or bromothymol blue (blue, right); their contents mix as evidenced by the coalesced droplet turning green (movie S7). In (C), the droplets contain a pH universal indicator and either 100 mM NaOH (left) or 100 mM HCl (right); upon coalescing, an acid-base neutralization reaction occurs (inset) until the coalesced droplet turns uniform as the indicator shows qualitatively (movie S8). We subtracted the background from all images. Scale bars, 1 mm.

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